Lesson objective to review

1
Lesson objective - to review Basic aerodynamics
relationships .the minimum level of fidelity
required for pre-concept and conceptual design
assessments of subsonic UAVs
Expectations - You will understand how to apply
the basics and to avoid unnecessary detail
16-1
2
Importance
These are the fundamental aerodynamic
relationships needed to define a subsonic air
vehicle for a UAV system
16-2
3
Forces
and geometry
Ct
16-3
4
Aerodynamic lift
Lift (L) Cl????q?Sref Cl?q?Sref (16.1)
Cl? lift curve slope (theoretrical 2??/rad
see RayAD Eq 12.6 for
more exact formulation) ? angle of
attack Sref aerodynamic reference area
Dynamic pressure (q) (?/2)?V2
(16.2) ? air density (lb-sec2/ft4) V
airspeed (ft/sec)
where
and
where
For uncambered airfoils Cl 0 at ? 0
?
V
16-4
5
Aerodynamic drag
Drag (D) Cd?q?Sref
(16.3) Cd drag coefficient
CdminCdi Cdmink?Cl-Clmin2 (16.4) k
1/??AR?e AR Aspect ratio b2/Sref e
Oswold wing efficiency f(?,AR) ?
sweep Cdmin Cf?Kd?(Swet/Sref) Cfe?(Swet/Sref)
(16.5) Cf flat plate skin friction
coefficient (See RayAD Fig
12.21) Kd ? 1.2 Factor to account for
non-friction drag items such as pressure and
interference) Cfe Equivalent skin friction
coefficient (RayAD12.3)
where
and
For uncambered airfoil Cdmin Cd0
where

• These relationships are for untrimmed drag
  polars, good aerodynamic design will minimize
  trim drag impact (which we will ignore for now)

16-5
6
Oswold efficiency factor
Source - Lee Nicolai, Conceptual Design Process,
LM Aero
16-6
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Lift and drag - contd

• CL? and Cdmin are approximately constant for
  low-to-medium subsonic speed range (below drag
  rise)
• This simplifying assumption makes our aero
  analysis task really easy (and reasonably correct)

16-7
8
L/D max - another perspective

• Theoretical (L/D)max
• If Cd Cd0 K?Cl2 then D/L Cd0/Cl K?Cl)
  and (L/D) max will occur when d(D/L)/dCl 0
• - Cd0/Cl2 K 0 or Cd0 K?Cl2 Cdi

or.
16-8
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L/D contd
16-9
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Notional example
A subsonic UAV has the following
characteristics W0/Sref 40 psf AR 20 ? 0
deg Swet/Sref 5 or b2/Swet 20/5 4 Cfe
.0035 From chart 16.6 at AR 20 and ? 0 deg, e
0.8 and Cd _at_ LoDmax 2?Cfe?(Swet/Sref)
.035 ? Cd0 .0175 Cl _at_ LoDmax sqrt
(??AR?e?Cdo) 0.938 LoDmax sqrt??e/Cfe?AR/(
Swet/Sref)/2 26.8 q _at_ LoDmax (W0/Sref)/Cl
42.6 psf EAS _at_ LoDmax 112.2 KEAS See Chapter
17 for definition of EAS and KEAS
16-10
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Correction factors

• For pre-concept studies, equations 16.1 - 16.5
  will yield reasonable estimates of lift and drag
• Nonetheless it is good practice to always compare
  estimates to data from similar aircraft and to
  apply appropriate correction factors

• Our previous calculation of LoDmax 26.8 for AR
  20, Swet/Sref 5, for example, when compared
  to parametric data from other aircraft shows that
  our estimate is consistent with the parametric
  data
• If not we could correct the estimate by putting a
  multiplier on Cdmin

LoDmax comparisons
35
30
25
20
(L/D)max
15
10
5
0
0
2
4
6
8
Wetted AR b2/Swet
Manned aircraft data LM Aero data handbook
16-11
12
More refined estimates

• For conceptual design studies, a component
  build-up method (see RayAD 12.5) will yield
  higher fidelity drag estimates and capture
• Reynolds number effects
• Overall and for individual components
• Form factor effects
• Such as wing thickness
• Interference drag effects
• Miscellaneous drag contributions
• As we will see later, our pre-concept design
  spread sheet methods could also incorporate these
  higher fidelity methods with little additional
  work
• They will be included at a later date
• A better approach for conceptual design would be
  a combination of component build up for trade
  studies and Euler CFD for baseline analysis

16-12
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Compressibility effects
On subsonic UAVs we can ignore compressibility
effects for lift and drag, but not for jet engine
performance - The effects are estimated assuming
a perfect gas, where specific heat ratio (?
1.4) Pressure effect P/Pa 1(?-1)/2?M2?/(
?-1) 10.2?M23.5 (16.11) Temperature
effect T/Ta 1(?-1)/2?M2 10.2?M2
(16.12) P and T Total
(isentropic stagnation) pressure and
temperature Pa and Ta Static atmospheric
pressure and temperature Example M 0.8
36Kft (Pa 472.6 psf Ta 390R) P/Pa 1.52 or
P 720 psf ( 27Kft _at_ M0) T/Ta 1.13 or T
440R -19.8F ( 22Kft _at_ M0)
where
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Example problem

• In Chapter 15 we assumed a nominal starting value
  of LoDcr LoDlo 23 for our example TBProp
• Assuming nominal values of Cfe 0.0035 and e
  0.8, from Chart 16-9
• (L/D)max sqrt??e/Cfe?b2/Swet/2
• or
• b2/Swet 23?22?Cfe/??e
  AR/Swet/Sref
• 2.95
• For a typical wing-body-tail configuration where
  Swet/Sref 5 (RayAD Fig 3.5), therefore, AR
  14.75
• This value would be at the upper range of AR for
  typical commercial regional TBProps
• The corresponding aerodynamic coefficients would
  be
• Cd0 Cfe?(Swet/Sref) 0.0175 (175 counts)
• Cl _at_ LoDmax sqrt (??AR?e?Cdo) 0.805

16-14
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Expectations

• You understand how to estimate basic subsonic
  aerodynamic performance
• Straight forward calculations based on
  aerodynamic smoothness and geometry
• Geometry implies achievable levels of
  aero-performance
• Associated lift and drag coefficients translate
  into design requirements

16-15
16
Homework (individual)

• 3. For your air vehicle configuration type,
  assume a representative value of Swet/Sref (RayAD
  Figure 3.5)
• Explain your rationale
• 4. Using the aerodynamic assumptions from Chart
  16-14 and homework problem 1, calculate AR, Cd0
  and Cl _at_ LoDmax
• Assess the reasonableness of your calculations

16-15
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Intermission
16-15